Phase coexistence in proton glass

Proton glasses are crystals of composition M{sub 1{minus}x}(NW{sub 4}){sub x}W{sub 2}AO{sub 4}, where M = K,Rb, W = H,D, A = P,As. For x = 0 there is a ferroelectric (FE) transition, while for x = 1 there is an antiferroelectric (AFE) transition. In both cases, the transition is from a paraelectric (PE) state of tetragonal structure with dynamically disordered hydrogen bonds to an ordered state of orthorhombic structure. For an intermediate x range there is no transition, but the hydrogen rearrangements slow down, and eventually display nonergodic behavior characteristic of glasses. The authors and other have shown from spontaneous polarization, dielectric permittivity, nuclear magnetic resonance, and neutron diffraction experiments that for smaller x there is coexistence of ferroelectric and paraelectric phases, and for larger x there is coexistence of antiferroelectric and paraelectric phases. The authors present a method for analytically describing this coexistence, and the degree to which this coexistence is spatial or temporal